Finite Group Databasebeta

← #14276948

Subgroups — #14276948

Order 1920.

328 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752343C211yesmaximal, characteristic
2C3×C4×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic
3#11746870C211yesmaximal, characteristic
4#10598544—31nomaximal, Hall
5C2×C3×C4⋊AGL(1,𝔽5)—21no—
6C2×C3×C4×AGL(1,𝔽5)C412yes—
7C3×C42×D5C2211yescharacteristic
8#91233C412yescomplemented
9#91232—21no—
10#91231—21no—
11C3×(C2×AGL(1,𝔽5))⋊C4—21no—
12#91087C411yescharacteristic, complemented
13C5×#803C411yescharacteristic, complemented
14#90982—21no—
15#90955—21no—
16#67621—51nomaximal, Hall
17C4×C4⋊AGL(1,𝔽5)D311yescharacteristic
18#65684—31no—
19#64994—31no—
20C22×C3×AGL(1,𝔽5)—22no—
21C2×C3×C4×D5C2×C411yescharacteristic
22C2×C3×C4×D5D411yescharacteristic
23C2×C3×C4×D5D411yescharacteristic
24C2×C3⋊#170—22no—
25C3×C4⋊AGL(1,𝔽5)—24no—
26C3×C4×AGL(1,𝔽5)—42no—
27C3×C42×C5C2×C411yescharacteristic
28C2×C3⋊#168—21no—
29C2×C5×C3⋊C8—21no—
30C3×C4×Dic5C2×C411yescharacteristic
31C3×C4×Dic5D411yescharacteristic
32C3×C4×Dic5Q811yescharacteristic
33C3×C4×C4⋊C4—51no—
34#4926—51no—
35#4926—51no—
36C2×C4⋊AGL(1,𝔽5)—21no—
37C2×C4×AGL(1,𝔽5)Dic312yes—
38C42×D5C2×D311yescharacteristic
39(C2×AGL(1,𝔽5))⋊C4—21no—
40#4004—32no—
41#4003—61no—
42#4002—61no—
43C5×#97—31no—
44#3952—61no—
45#3946—61no—
46#3935—31no—
47#1285—151noSylow
48C22×C3×D5C22⋊C411yescharacteristic
49C2×C3×AGL(1,𝔽5)—24no—
50C2×C3×AGL(1,𝔽5)—42no—
51C2×C3×AGL(1,𝔽5)—42no—
52C2×C3×C4×C5C4211yescharacteristic
53C2×C3×C4×C5C22⋊C411yescharacteristic
54C2×C3×C4×C5C4⋊C411yescharacteristic
55C2×C3×Dic5C22⋊C411yescharacteristic
56C2×C3×Dic5C4⋊C411yescharacteristic
57C2×C3×Dic5C4⋊C411yescharacteristic
58C3×C4×D5—21no—
59C3×C4×D5—21no—
60C3×C4×D5—22no—
61C3×C4×D5—41no—
62C3⋊#170—42no—
63C3⋊#168—41no—
64C5×C3⋊C8—41no—
65C2×C3×C4⋊C4—101no—
66C2×C3×C42—51no—
67C2×C3×C42—52no—
68C3×#95—101no—
69#830—101no—
70#830—101no—
71C4⋊(C3⋊C8)—52no—
72C4⋊(C3⋊C8)—101no—
73#803—51no—
74#803—101no—
75#803AGL(1,𝔽5)11yescharacteristic, complemented
76C22×AGL(1,𝔽5)—22no—
77C2×C4×D5C2×Dic311yescharacteristic
78C2×C4×D5#6711yescharacteristic
79C2×C4×D5#6711yescharacteristic
80C2×#170—62no—
81C4⋊AGL(1,𝔽5)—24no—
82C4×AGL(1,𝔽5)—42no—
83C2×C5×C8—61no—
84C42×C5C4×D311yescharacteristic
85C4×Dic5Dic611yescharacteristic
86C4×Dic5C4×D311yescharacteristic
87C4×Dic5D1211yescharacteristic
88C2×#168—61no—
89#432—151no—
90#432—151no—
91C4×C4⋊C4—51no—
92C22×C3×C5#9511yescharacteristic
93C2×C3×D5—21no—
94C2×C3×D5—21no—
95C2×C3×D5#10011yescharacteristic
96C2×C3×D5#10111yescharacteristic
97C3×AGL(1,𝔽5)—44no—
98C3×C4×C5—21no—
99C3×C4×C5—21no—
100C3×C4×C5—21no—
101C3×Dic5—21no—
102C3×Dic5—21no—
103C3×Dic5#10412yes—
104C22×C3×C4—51no—
105C22×C3×C4—51no—
106C22×C3×C4—51no—
107C22×C3×C4—102no—
108C3×C4⋊C4—104no—
109C3×C42—51no—
110C3×C42—51no—
111C3×C42—51no—
112C3×C42—202no—
113C3×C42C2×AGL(1,𝔽5)11yescharacteristic
114C2×C3⋊C8—21no—
115C2×C3⋊C8—102no—
116C2×C3⋊C8—101no—
117C22×D5#21711yescharacteristic
118C2×AGL(1,𝔽5)—24no—
119C2×AGL(1,𝔽5)—42no—
120C2×AGL(1,𝔽5)—42no—
121C2×C4×C5C4×Dic311yescharacteristic
122C2×C4×C5Dic3⋊C411yescharacteristic
123C2×C4×C5(C2×D3)⋊C411yescharacteristic
124C2×Dic5Dic3⋊C411yescharacteristic
125C2×Dic5C4⋊Dic311yescharacteristic
126C2×Dic5(C2×D3)⋊C411yescharacteristic
127C4×D5—21no—
128C4×D5—21no—
129C4×D5—22no—
130C4×D5—41no—
131#170—122no—
132C5×C8—121no—
133#168—121no—
134C2×C4⋊C4—101no—
135C2×C42—51no—
136C2×C42—52no—
137C4⋊C8—152no—
138C4⋊C8—301no—
139C22⋊C8—301no—
140C22⋊C8—301no—
141#97—31no—
142#97—151no—
143#97—301no—
144#95—101no—
145C2×C3×C5H(3,ℤ/4)11yescharacteristic
146C2×C3×C5#33911yescharacteristic
147C2×C3×C5#34311yescharacteristic
148C3×D5—21no—
149C3×D5—21no—
150C23×C3—51no—
151C2×C3×C4—51no—
152C2×C3×C4—51no—
153C2×C3×C4—51no—
154C2×C3×C4—102no—
155C2×C3×C4—101no—
156C2×C3×C4—101no—
157C2×C3×C4—104no—
158C2×C3×C4—201no—
159C2×C3×C4—202no—
160C2×C3×C4—202no—
161C2×C3×C4C4×AGL(1,𝔽5)11yescharacteristic
162C2×C3×C4C4⋊AGL(1,𝔽5)11yescharacteristic
163C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
164C3⋊C8—41no—
165C3⋊C8—201no—
166C3⋊C8—202no—
167C22×C5C3⋊#9511yescharacteristic
168C2×D5—21no—
169C2×D5—21no—
170C2×D5#83311yescharacteristic
171C2×D5#83611yescharacteristic
172AGL(1,𝔽5)—44no—
173C4×C5—21no—
174C4×C5—21no—
175C4×C5—21no—
176Dic5—21no—
177Dic5—21no—
178Dic5#80512yes—
179C22×C4—51no—
180C22×C4—51no—
181C22×C4—51no—
182C22×C4—102no—
183C2×C8—61no—
184C2×C8—302no—
185C2×C8—301no—
186C4⋊C4—104no—
187C42—51no—
188C42—51no—
189C42—51no—
190C42—202no—
191C42D3×AGL(1,𝔽5)11yescharacteristic
192C3×C5#128511yescharacteristic, complemented, Hall
193C22×C3—51no—
194C22×C3—51no—
195C22×C3—101no—
196C22×C3—101no—
197C22×C3(C2×AGL(1,𝔽5))⋊C411yescharacteristic
198C3×C4—21no—
199C3×C4—21no—
200C3×C4—21no—
201C3×C4—52no—
202C3×C4—101no—
203C3×C4—101no—
204C3×C4—204no—
205C2×C5#452311yescharacteristic
206C2×C5#453011yescharacteristic
207C2×C5#453111yescharacteristic
208D5—21no—
209D5—21no—
210C23—51no—
211C2×C4—51no—
212C2×C4—51no—
213C2×C4—51no—
214C2×C4—102no—
215C2×C4—101no—
216C2×C4—101no—
217C2×C4—104no—
218C2×C4—201no—
219C2×C4—202no—
220C2×C4—202no—
221C2×C4Dic3×AGL(1,𝔽5)11yescharacteristic
222C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
223C2×C4Dic3⋊AGL(1,𝔽5)11yescharacteristic
224C8—121no—
225C8—601no—
226C8—602no—
227C2×C3—101no—
228C2×C3—101no—
229C2×C3#6486311yescharacteristic
230C2×C3#6489911yescharacteristic
231C2×C3#6490011yescharacteristic
232C5#6762111yescharacteristic, complemented, Sylow
233C22—51no—
234C22—51no—
235C22—101no—
236C22—101no—
237C22(C2×AGL(1,𝔽5))⋊Dic311yescharacteristic
238C4—21no—
239C4—21no—
240C4—21no—
241C4—52no—
242C4—101no—
243C4—101no—
244C4—204no—
245C3#1059854411yescharacteristic, complemented, Sylow
246C2—101no—
247C2—101no—
248C2#1174651811yescharacteristic
249C2#1174652711yescharacteristic
250C2#1174653411yescharacteristic
subgroupG/H
centerC22(C2×AGL(1,𝔽5))⋊Dic3
commutatorC2×C3×C4×C5C42
Frattini, hypercenterC42D3×AGL(1,𝔽5)
FittingC3×C42×C5C2×C4
socleC22×C3×C5#95
prime radicalC22×C3×D5C22⋊C4
cosocleC3×C42×D5C22
hypocenterC3×C5#1285
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
8. #91233C4semidirect
12. #91087C4semidirect
13. C5×#803C4semidirect
75. #803AGL(1,𝔽5)semidirect
192. C3×C5#1285semidirect
232. C5#67621semidirect
245. C3#10598544semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#117523432
C3×C4×C4⋊AGL(1,𝔽5)2
#117468702
#105985443
#676215